“Can” and “able to” are the same in the present tense:
Yes, I can take on this project.
Yes, I’m able to take on this project.
The negative forms are can’t and not able to – or unable to:
Can/can’t are more informal and more common in everyday speaking. Able to and not able to / unable to are a little more formal.
In the past, we use could/couldn’t or was/wasn’t able to (or was unable to):
In general, both are used in the negative form:
But in the positive form, “was able to” is a little more common than “could”:
In the future, there is only will/won’t be able to. Don’t say “will can” or “won’t can” – it’s a common error in English!
When you are making a polite request for someone to do something, use “could” (more formal) or “can” (more informal):
When asking about someone’s abilities, you can use either CAN or ABLE TO:
Can is probably more common in spoken English, simply because it’s shorter.